Abstract
In this paper we introduce the concept of the genus of a birational mapping of nonsingular three-dimensional algebraic varieties over a field of characteristic 0 and prove that the automorphisms whose genus is at most a fixed number form a group. We also prove that a birational morphism of nonsingular three-dimensional varieties splits into a composition of a map which is an inverse to a morphism of genus 0 and monoidal transformations. Bibliography: 9 items.
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